Method for detecting damage position and degree of buckling restrained brace

Abstract

The invention belongs to the technical field of buckling restrained brace damage detection, and particularly discloses a method for detecting the damage position and degree of a buckling restrained brace, and the method comprises the steps: collecting a reference signal of a buckling restrained brace under an undamaged working condition, obtaining a signal under each damaged working condition through a fatigue test, and extracting modal features; based on the modal features, establishing a mathematical relationship model of the modal curvature difference and the wavelet coefficient difference with the damage degree; actual damaged buckling restrained brace signals are collected, modal information is extracted, a modal curvature difference method based on statistics and wavelet coefficient difference analysis are adopted to determine the damage position, and the modal curvature difference and the wavelet coefficient difference corresponding to the damage position are extracted; and determining the damage degree according to the mathematical relationship model of the modal curvature difference, the wavelet coefficient difference and the damage degree, the modal curvature difference and the wavelet coefficient difference. The problems that an existing buckling restrained brace damage detection method cannot accurately recognize the damage position, cannot evaluate plastic deformation, and is high in detection cost and complex in operation are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of buckling restraint brace damage detection, and in particular relates to a method for detecting the damage position and degree of a buckling restraint brace. Background Art

[0002] Buckling-restrained braces (BRBs) are vibration-damping devices widely used in engineering fields closely related to urban resilience, such as high-rise buildings, bridge structures, and critical infrastructure. Properly configured BRBs can significantly reduce a structure's dynamic response under seismic excitation, effectively alleviating damage to primary structural components and thus improving the building's overall seismic performance. With the implementation of relevant policies, BRBs have become mandatory for certain critical buildings.

[0003] Buckling-restrained braces dissipate external energy through the tension and compression of their internal materials. When subjected to certain forces, these braces can become damaged. After a certain period of service, these braces require routine inspection. Determining the location and extent of damage is a critical step in this routine inspection. Therefore, a method for detecting the location and extent of damage in buckling-restrained braces is needed.

[0004] Currently, the most direct method for assessing buckling-restrained brace damage is to measure the mechanical properties of internal components. An existing buckling-restrained brace damage detection method employs a detection device to monitor the subsequent performance of dampers under multiple stress states and high and low temperature environments. However, this method requires the dampers to be installed within the device for testing. Removing the buckling-restrained brace from the structure after an earthquake is not feasible. Furthermore, buckling-restrained brace damage is irreversible, meaning that the damage may have worsened after testing. This approach is meaningless for assessing post-earthquake service life. Another approach involves nondestructive testing (NDT). An X-ray-based NDT device for steel structures has been designed and installed on a positioning and conveying device for conveying steel structures. This allows for continuous inspection of the steel structure, reducing operator workload and improving NDT efficiency. However, after an earthquake, the buckling-restrained brace will be damaged due to plastic deformation of the component. X-rays can only detect internal defects, but not plastic deformation. Furthermore, this method requires expensive equipment and is highly specialized, resulting in high learning and application costs. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems that the existing buckling restraint support damage detection method cannot accurately identify the damage location, cannot evaluate plastic deformation, and has high detection costs and complex operations. A method for detecting the damage location and extent of buckling restraint supports is proposed.

[0006] The technical solution of the present invention is: a method for detecting the damage location and degree of a buckling restrained brace, comprising the following steps: The baseline signal of the buckling restrained support under undamaged working conditions is collected, and the signals under various damaged working conditions are obtained through fatigue testing. The baseline signal and the signals under various damaged conditions are subjected to Fourier transform to extract modal features. Based on the modal characteristics, a mathematical relationship model between the modal curvature difference and wavelet coefficient difference and the damage degree is established, where the modal curvature difference and wavelet coefficient difference are the parameter differences between the current working condition and the intact working condition; Collect the actual damaged buckling restraint support signal and extract the modal information of the actual damaged buckling restraint support; Based on the modal information of the actual damaged buckling restrained support, the normal distribution of the modal information is constructed and combined with the curve mutation analysis to determine the damage location, and the modal curvature difference and wavelet coefficient difference corresponding to the damage location are extracted; The damage degree is determined based on the mathematical relationship model between the modal curvature difference, wavelet coefficient difference and damage degree, as well as the modal curvature difference and wavelet coefficient difference corresponding to the damage location.

[0007] Preferably, the reference signal of the buckling restrained support under undamaged working condition is collected, the signal under each damaged working condition is obtained through fatigue testing, and the modal characteristics are extracted by Fourier transform of the reference signal and the signal under each damaged state, specifically: The components of the buckling restraint support are divided into multiple units, magnetic bases are set at the intervals between the units, and sensors are installed on the magnetic bases. The sensors are connected to the data acquisition system through cables. Based on the sampling frequency, duration, and amplitude set by the data acquisition system, sensors are used to collect the baseline signal of the buckling restrained brace under intact working conditions, as well as the signals under various damaged working conditions during the fatigue test. The reference signal and the signals in each damage state are converted into frequency domain signals through fast Fourier transform; Calculate the average spectrum of each frequency domain signal and identify the natural frequency from the average spectrum; Extract the complex response of each measurement point at the identified natural frequency and calculate the amplitude and phase; The point with the maximum amplitude in the average spectrum is selected as the reference point, and the vibration mode value of the reference point is set to 1. The vibration mode values ​​of other positions are the ratios of the amplitudes of other positions to the amplitude of the reference point. The vibration mode direction is determined based on the phase difference between other positions and the reference point. Finally, the complete vibration mode is obtained to complete the modal feature extraction.

[0008] Preferably, the specific calculation formula for converting the signal into the frequency domain by fast Fourier transform is:

[0009] in, Indicates the first outputs, Indicates the first input samples, represents the number of sample points, Represents an imaginary unit , represents the natural base, Represents pi.

[0010] Preferably, the calculation formula of the amplitude is:

[0011] in, Indicates the first The amplitude of the output, Indicates the first The real part of the output, Indicates the first The imaginary part of the output; The calculation formula of the phase is:

[0012] in, Indicates the first The phase angle of the output, Represents the inverse tangent function.

[0013] Preferably, the method for establishing a mathematical relationship model between the modal curvature difference and the wavelet coefficient difference and the damage degree is: The Miner linear damage theory criterion is used to calculate the damage value of each part of the buckling restrained brace; Through fatigue tests, acceleration signals under different fatigue states are obtained. Specifically, the damage value of the buckling restraint support core component in the corresponding state is calculated, and then the modal curvature difference and wavelet coefficient difference under the corresponding damage state are calculated; there is a quadratic function relationship between the damage value and the modal curvature difference and wavelet coefficient difference. The modal curvature difference and wavelet coefficient difference are exponentially fitted, and a fitting equation is established to obtain a mathematical relationship model between the modal curvature difference, wavelet coefficient difference and the damage degree.

[0014] Preferably, the damage value of each part of the buckling restrained support is:

[0015] in, Indicates the damage value, that is, the degree of damage, To maintain the The number of loading cycles when the component fails at the first stress level, For the The number of loading cycles of the component under the stress level is Indicates the Level stress condition.

[0016] Preferably, the normal distribution of the modal information is constructed and combined with curve mutation analysis to determine the damage location, specifically: Obtain the modal characteristics of the intact component and the component to be tested, calculate the modal curvature of the intact component and the component to be tested respectively, and then perform wavelet transform on the modal curvature to enhance the local feature extraction of the modal curvature to obtain the wavelet coefficients of the intact component and the component to be tested; Calculating the modal curvature difference based on the modal curvatures of the undamaged component and the component to be measured, and calculating the wavelet coefficient difference based on the wavelet coefficients of the undamaged component and the component to be measured; Construct the normal distribution of the modal curvature and wavelet coefficients of the intact component and the component to be tested, and then construct the normal distribution of the modal curvature difference and wavelet coefficient difference; Normalizing each parameter in the normal distribution of the modal curvature difference and the wavelet coefficient difference to obtain the standard quantile of the modal curvature difference and the standard quantile of the wavelet coefficient difference; If the standard quantile of the modal curvature difference and the standard quantile of the difference between the wavelet coefficients Stay within the confidence interval, that is and When , it is determined that no damage occurs; otherwise, it is determined that damage occurs; The confidence level is The upper quantile of the modal curvature difference, The confidence level is The upper quantile of the wavelet coefficient difference, represents the significance level; The modal curvature difference and wavelet coefficient difference curves are plotted to detect the mutation points in the curves. The mutation points are the damage locations of the buckling restraint support components.

[0017] Preferably, the calculation formula of the modal curvature difference is:

[0018]

[0019] in, Buckling restrained brace members Level The modal curvature of the element, Buckling restrained brace members Level -1 element modal displacement, Buckling restrained brace members Level The modal displacement of each element, Buckling restrained brace members Level +1 element modal displacement, is the cell length, for Level The modal curvature difference of each element is For the component under test Level The modal curvature of the element, Undamaged components Level The modal curvature of each element; The calculation formula of the wavelet coefficient difference is:

[0020]

[0021] in, is the wavelet coefficient, is the complex conjugate of the wavelet function, Indicates the modal curvature with the measuring point position The function of change, is the translation factor, is the change of the measuring point, is the wavelet coefficient difference, is the wavelet coefficient of the component to be tested, is the wavelet coefficient of the undamaged component, Represents the scale index, which is used to control the scaling degree of the wavelet.

[0022] Preferably, the normal distribution of the modal curvature and wavelet coefficients of the intact component and the component to be tested is constructed as follows:

[0023]

[0024] in, Buckling restrained brace members Level The mean of the modal curvatures of the elements, Buckling restrained brace members Level The variance of the modal curvature of each element, is the wavelet coefficient The mean of is the wavelet coefficient The variance of Indicates the number of sample points; The normal distribution of the constructed modal curvature difference and wavelet coefficient difference is specifically:

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] in, for Level The mean of the modal curvature differences of the elements, for Level The variance of the modal curvature difference of each element, is the mean of the wavelet coefficient differences, is the variance of the wavelet coefficient difference, For the component under test Level The mean of the modal curvatures of the elements, For the component under test Level The mean of the modal curvatures of the elements, For the component under test Level The variance of the modal curvature of each element, For the component under test Level The variance of the modal curvature of each element, is the mean value of the wavelet coefficients of the component to be tested, is the mean of the wavelet coefficients of the undamaged component, is the variance of the wavelet coefficients of the component to be tested, is the variance of the wavelet coefficients of the undamaged component.

[0031] Preferably, the specific calculation formula for the standard quantile of the modal curvature difference is:

[0032] in, is the standard quantile of the modal curvature difference; The specific calculation formula for the standard quantile of the wavelet coefficient difference is:

[0033] in, is the standard quantile of the wavelet coefficient difference, which is used to evaluate the distance between the sample point and the overall mean.

[0034] The beneficial effects of the present invention are: 1. By combining modal curvature differences and wavelet coefficient differences, the present invention effectively addresses the challenges of complex structures. For example, in buckling-restrained braces, the structure may exhibit inherent characteristics such as sudden cross-sectional changes, strain concentration, or material inhomogeneity. These characteristics can lead to false sudden changes in wavelet coefficient differences or modal curvature differences in the absence of damage, thereby misjudging the damage location. The combined algorithm of the present invention significantly reduces the false positive rate through complementary mechanisms (for example, the high resolution of wavelet coefficient differences compensates for the low sensitivity of modal curvature differences), making the proposed method more applicable to real-world engineering scenarios.

[0035] 2. The present invention introduces a probability-based damage identification method, which converts the identification of damage location and index into a probability distribution estimate. This method is particularly suitable for test scenarios because even specimens of the same size and material can produce slight differences due to manufacturing errors, material inhomogeneities, or environmental factors (such as temperature fluctuations). These differences may be misjudged as damage by deterministic methods. The probability-based method eliminates these random errors through statistical modeling, achieving more reliable identification. In addition, existing methods usually require a reference signal from an undamaged specimen as a reference, but it is difficult to obtain exactly the same undamaged specimen in actual engineering. The present invention allows the use of signals from similar specimens (such as the same size and material) and compensates for the differences through probabilistic correction, thereby extending the method from a simulation environment to actual test scenarios, thereby solving the pain point of existing methods - the strict reliance on reference signals.

[0036] 3. Through joint analysis (such as wavelet transform-enhanced local feature extraction of modal curvature), the present invention solves the problems of the single modal curvature difference method, which mainly relies on the accurate measurement of modal shape and is highly sensitive to measurement noise, changes in boundary conditions and the accuracy of low-order modes, resulting in large deviations in the damage index in a noisy environment; and the single wavelet coefficient difference method, which is overly sensitive to damage and may misjudge slight noise, microscopic material unevenness or environmental vibration as damage, resulting in overfitting and false positive results, making the damage value calculation closer to reality.

[0037] 4. The present invention does not require the establishment of a costly health monitoring system and platform. Only a one-time detection is required to quickly assess the location and extent of damage, and can accurately locate the specific damage location of the buckling restrained support and quantify the damage value.

[0038] 5. The present invention can address the pain points of buckling restraint brace damage identification (such as misjudgment, noise sensitivity, and test errors), and realizes a completely non-destructive testing method. It can complete the inspection and evaluation without causing any damage to the buckling restraint brace, and can detect plastic deformation with simple operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 The figure shows a flow chart of a method for detecting the damage location and degree of a buckling restrained brace provided in Example 1 of the present invention.

[0040] Figure 2 Shown is a schematic diagram of the composition of the buckling restraint support provided in Example 1 of the present invention.

[0041] Figure 3 Shown is a plan view of the core component of the buckling restrained support provided in Example 1 of the present invention.

[0042] Figure 4 Shown is a plan view of the restraining component of the buckling restraining support provided in Example 1 of the present invention.

[0043] Figure 5 Shown is a vertical view of the restraining component of the buckling restraining support provided in Example 1 of the present invention.

[0044] Figure 6 Shown is a schematic diagram of a system for detecting the location and extent of damage to a buckling restrained brace provided in Example 2 of the present invention.

[0045] Figure 7 Shown is a mathematical model curve diagram of modal curvature difference and damage value provided by Example 3 of the present invention.

[0046] Figure 8 Shown is a mathematical model curve diagram of wavelet coefficient difference and damage value provided by Example 3 of the present invention.

[0047] Figure 9 Shown is a curve diagram of modal curvature varying with position provided by Example 4 of the present invention.

[0048] Figure 10 The figure shows a curve diagram of the wavelet coefficients varying with position provided by Example 4 of the present invention.

[0049] Figure 11 Shown is a curve diagram of the modal curvature difference and wavelet coefficient difference varying with position provided by Example 4 of the present invention.

[0050] Explanation of the accompanying reference numerals: 1—core component, 2—constraint member, 11—connecting plate, 12—stiffening plate, 13—core material, 3—data acquisition system, 4—sensor, 5—excitation device. DETAILED DESCRIPTION

[0051] The exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the accompanying drawings are merely exemplary and are intended to illustrate the principles and spirit of the present invention, rather than to limit the scope of the present invention.

[0052] Example 1: like Figure 1 As shown, a method for detecting the damage location and extent of a buckling restrained brace includes the following steps: S1. Collect a baseline signal of the buckling restrained brace under intact working conditions, obtain signals under various damaged working conditions through fatigue testing, and perform Fourier transform on the baseline signal and the signals under various damaged conditions to extract modal features; S2. Based on the modal characteristics, a mathematical relationship model is established between the modal curvature difference and wavelet coefficient difference and the damage degree, where the modal curvature difference and wavelet coefficient difference are the parameter differences between the current working condition and the intact working condition; S3. collecting actual damaged buckling restraint support signals and extracting modal information of the actual damaged buckling restraint support; S4. Based on the modal information of the actual damaged buckling restrained brace, construct a normal distribution of the modal information and combine it with curve catastrophe analysis to determine the damage location. Then, extract the modal curvature difference and wavelet coefficient difference corresponding to the damage location. S5. Determine the damage extent based on the mathematical relationship model between the modal curvature difference, wavelet coefficient difference and damage extent, and the modal curvature difference and wavelet coefficient difference corresponding to the damage location.

[0053] Traditional damage detection methods primarily target relatively simple structures, typically with uniform cross-sections and low complexity, resulting in relatively simple damage patterns. This paper designs a nondestructive testing method for complex structures such as buckling-restrained braces (BRBs), which are widely used in earthquake engineering and often involve complex factors such as nonlinear behavior, stress concentration, and dynamic response.

[0054] like Figure 2 、 Figure 3 、 Figure 4 and Figure 5 As shown in Figure 1, the buckling restrained brace mainly consists of five core parts, including: Core material 13: The core plate is an axial load-bearing component responsible for providing the main bearing capacity and energy dissipation capacity of the support; Connecting plate 11: acts as a transitional member between the core plate and the structure, transferring forces; Stiffening plate 12: connected to the connecting plate to prevent the connecting plate from being damaged prematurely and ensure structural integrity; Restraint 2: An external member surrounding the core material, usually made of steel tube or concrete-filled steel tube, which prevents the core material from buckling when compressed; Isolation layer: Located between the core 13 and the restraining member 2, it allows the core 13 to deform freely in the axial direction while reducing friction and lateral restraint. This structural design enables the buckling-restrained brace to maintain stable hysteretic properties under cyclic tension and compression loads, effectively dissipating seismic energy.

[0055] The core plate 13, the connecting plate 11 and the stiffening plate 12 are welded together to form a whole, which is referred to as the core component 1 in the embodiment of the present invention. This core component 1 not only determines the mechanical properties of the buckling restrained brace, but is also the component most susceptible to damage.

[0056] In this embodiment, the reference signal of the buckling restrained support under intact working condition is collected, the signal under each damaged working condition is obtained through fatigue testing, and the modal features are extracted by Fourier transform of the reference signal and the signal under each damaged state, specifically: The components of the buckling restraint support are divided into multiple units, magnetic bases are set at the intervals between the units, and sensors 4 are installed on the magnetic bases. The sensors 4 are connected to the data acquisition system through cables. Based on the sampling frequency, duration, and sampling amplitude set by the data acquisition system 3, the reference signal of the intact buckling restrained support is collected through the sensor 4. The time domain signal of each sensor 4 is converted to the frequency domain through the fast Fourier transform. Since the signal being processed is discrete, the discrete Fourier transform is used:

[0057] in, Indicates the first outputs, Indicates the first input samples, represents the number of sample points, Represents an imaginary unit ; Calculate the average spectrum of each frequency domain signal and identify the natural frequency from the average spectrum; Select the appropriate modal order according to the characteristics of the excitation device 5, usually giving priority to low-order modes; The complex response of each measurement point is extracted at the identified natural frequency, and the amplitude and phase are calculated. The amplitude calculation formula is:

[0058] in, Indicates the first The amplitude of the output, Indicates the first The real part of the output, Indicates the first The imaginary part of the output; The calculation formula of the phase is:

[0059] in, Indicates the first The phase angle of the output; The point with the maximum amplitude in the average spectrum is selected as the reference point, and the vibration mode value of the reference point is set to 1. The vibration mode values ​​of other positions are the ratios of the amplitudes of other positions to the amplitude of the reference point. The vibration mode direction is determined based on the phase difference between other positions and the reference point. Finally, the complete vibration mode is obtained to complete the modal feature extraction.

[0060] In this embodiment, a fatigue test loading system for buckling restrained braces is specified, which meets the fatigue performance test requirements of the "Technical Specification for Application of Buckling Restrained Braces" (T / CECS 817-2021). The fatigue test includes the following steps: Step 1: Before the specimen yields, force control is used and loading is divided into two levels, with each level being loaded back and forth for one circle.

[0061] Step 2: After the specimen yields, displacement-controlled loading is adopted, and reciprocating loading is performed for 2 cycles at 2 times the yield displacement and 4 times the yield displacement.

[0062] Step 3: After the specimen yields, it should be reciprocated for 30 cycles at the product design fatigue displacement.

[0063] Step 4: Reciprocate load for 3 cycles at 1.2 times the product design fatigue displacement.

[0064] Step 5: If the cumulative plastic ductility coefficient is less than 1200 after completing the reciprocating loading of steps 1 to 4, continue reciprocating loading at the product design fatigue displacement until the component breaks. Record the number of loading cycles and stop loading after every 30 cycles.

[0065] The test requires the installation of strain gauges within each unit cell, as well as the placement of displacement and force sensors near the connecting plates. The test results will display the overall deformation and force output of the buckling-restrained brace, as well as the strain-time history curve for each unit cell.

[0066] In this embodiment, the method for establishing a mathematical relationship model between the modal curvature difference and the wavelet coefficient difference and the damage degree is: The Miner linear damage theory criterion is used to calculate the damage value of each part of the buckling restrained support:

[0067] in, Indicates the damage value, that is, the degree of damage, To maintain the The number of loading cycles when the component fails at the first stress level, For the The number of loading cycles of the component under the stress level is Indicates the Grade 2 stress level conditions; Fatigue testing yields acceleration signals under different fatigue conditions. Specifically, the damage value of the core component corresponding to the state is calculated, followed by the modal curvature difference and wavelet coefficient difference under the corresponding damage state. Since the damage value has a quadratic function relationship with the modal curvature difference and wavelet coefficient difference, an exponential fit is performed on the modal curvature difference and wavelet coefficient difference, establishing a fitting equation to derive a mathematical relationship model between the modal curvature difference and wavelet coefficient difference and the degree of damage. In subsequent testing phases, the corresponding wavelet coefficients and curvature modal differences are obtained to determine the damage value of the buckling restraint support.

[0068] In this embodiment, the normal distribution of modal information is constructed and combined with curve mutation analysis to determine the damage location, specifically: Obtain the modal characteristics of the intact component and the component to be tested, calculate the modal curvature of the intact component and the component to be tested respectively, and then perform wavelet transform on the modal curvature to enhance the local feature extraction of the modal curvature to obtain the wavelet coefficients of the intact component and the component to be tested; Calculating the modal curvature difference based on the modal curvatures of the undamaged component and the component to be measured, and calculating the wavelet coefficient difference based on the wavelet coefficients of the undamaged component and the component to be measured; The calculation formula of the modal curvature difference is:

[0069]

[0070] in, Buckling restrained brace members Level The modal curvature of the element, Buckling restrained brace members Level -1 element modal displacement, Buckling restrained brace members Level The modal displacement of each element, Buckling restrained brace members Level +1 element modal displacement, is the cell length, for Level The modal curvature difference of each element is For the component under test Level The modal curvature of the element, Undamaged components Level The modal curvature of each element; The calculation formula of the wavelet coefficient difference is:

[0071]

[0072] in, is the wavelet coefficient, is the complex conjugate of the wavelet function, Indicates the modal curvature with the measuring point position The function of change, is the translation factor, is the change of the measuring point, is the wavelet coefficient difference, is the wavelet coefficient of the component to be tested, is the wavelet coefficient of the undamaged component, Represents the scale index, which is used to control the scaling degree of the wavelet; Due to factors such as the environment and excitation, the modal curvature and wavelet coefficients obtained by calculation are discrete. In this case, it is assumed that the modal curvature and wavelet coefficients conform to the normal distribution:

[0073]

[0074] in, Buckling restrained brace members Level The mean of the modal curvatures of the elements, Buckling restrained brace members Level The variance of the modal curvature of each element, is the wavelet coefficient The mean of is the wavelet coefficient The variance of Indicates the number of sample points; When there is a difference between the wavelet coefficient or modal curvature of the test piece and the undamaged test piece, it is considered that the test piece is damaged. Since both conform to the normal distribution, the modal curvature difference and the wavelet coefficient difference conform to the normal distribution:

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] in, for Level The mean of the modal curvature differences of the elements, for Level The variance of the modal curvature difference of each element, is the mean of the wavelet coefficient differences, is the variance of the wavelet coefficient difference, For the component under test Level The mean of the modal curvatures of the elements, For the component under test Level The mean of the modal curvatures of the elements, For the component under test Level The variance of the modal curvature of each element, For the component under test Level The variance of the modal curvature of each element, is the mean value of the wavelet coefficients of the component to be tested, is the mean of the wavelet coefficients of the undamaged component, is the variance of the wavelet coefficients of the component to be tested, is the variance of the wavelet coefficients of the undamaged component; Normalizing each parameter in the normal distribution, we can obtain the standard quantile of the modal curvature difference and the standard quantile of the wavelet coefficient difference. The specific calculation formula is:

[0081]

[0082] in, is the standard quantile of the modal curvature difference, is the standard quantile of the wavelet coefficient difference, which is used to evaluate the distance from the sample point to the overall mean. and Stay within the confidence interval, that is and When , no damage occurs; otherwise, damage occurs; The confidence level is The upper quantile of the modal curvature difference, The confidence level is The upper quantile of the wavelet coefficient difference, represents the significance level; Plot modal curvature difference and wavelet coefficient difference curves, and detect the mutation points in the curves. These mutation points are the locations of damage to the core components. Based on the established damage model, the modal curvature difference and wavelet coefficient difference at the mutation points are used to quantitatively assess the damage extent at each damage location.

[0083] The proposed method, by combining modal curvature differences and wavelet coefficient differences, can effectively address the challenges of complex structures. For example, in buckling-restrained braces, the structure may exhibit inherent characteristics such as sudden cross-sectional changes, strain concentrations, or material inhomogeneities. These characteristics can lead to false abrupt changes in wavelet coefficient differences or modal curvature differences in the absence of damage, leading to misjudgment of damage locations. The combined algorithm proposed in this paper significantly reduces the false positive rate through complementary mechanisms (for example, the high resolution of wavelet coefficient differences compensates for the low sensitivity of modal curvature differences), making the method more applicable to real-world engineering scenarios.

[0084] Compared to existing methods, this method extends beyond simple to complex structures, achieving generalized damage identification capabilities. Experimental results show that in simulations of buckling-restrained braces under complex loads, this method improves position identification accuracy by over 15%, avoiding the misidentification of non-damage mutations by existing methods.

[0085] Existing methods rely solely on a single metric (such as modal curvature difference or wavelet coefficient difference) to identify damage locations and damage indices, which can easily lead to errors in complex structures. This invention innovatively combines the two to form a composite damage index calculation framework. The single modal curvature difference method relies primarily on accurate modal shape measurements and is highly sensitive to measurement noise, changes in boundary conditions, and the accuracy of low-order modes, leading to significant damage index deviations in noisy environments. The single wavelet coefficient difference method is overly sensitive to damage and may misinterpret slight noise, microscopic material inhomogeneities, or environmental vibrations as damage, resulting in overfitting and false-positive results. This invention utilizes a combined analysis (such as wavelet transform-enhanced local feature extraction of modal curvature) to make damage value calculation more realistic. This combined approach significantly improves the robustness of damage identification. Experimental validation demonstrates that, under the same damage simulation conditions, the goodness of fit (R² value) between the damage index and the actual damage extent of this method improves from 0.75 for existing methods to 0.92, reducing the systematic errors introduced by single methods. This not only improves accuracy but also expands the method's applicability in high-noise environments.

[0086] Furthermore, existing methods often employ deterministic frameworks and fail to account for the impact of random errors, making them difficult to generalize to actual testing. This present invention introduces a probabilistic damage identification method, transforming the identification of damage location and index into a probability distribution estimate. This method is particularly well-suited for testing scenarios, as even specimens of identical size and material can exhibit subtle differences due to manufacturing errors, material inhomogeneities, or environmental factors (such as temperature fluctuations). These differences can be misidentified as damage by deterministic methods. Probabilistic methods eliminate these random errors through statistical modeling, achieving more reliable identification. Furthermore, existing methods typically require a reference signal from an undamaged specimen, but obtaining identical undamaged specimens is difficult in actual engineering. This present invention allows the use of signals from similar specimens (e.g., of identical size and material) and compensates for these differences through probabilistic correction, thus extending the method from simulation environments to actual testing scenarios. This addresses the existing method's strict reliance on a reference signal. In experiments, using this probabilistic approach, the present invention reduced the false positive rate of damage identification by 20% in a group of specimens with a manufacturing error of ±5%. This method can also be directly applied to field testing without the need for an idealized undamaged reference signal. This greatly improves the engineering practicality and promotion potential of the method.

[0087] Example 2: Based on Example 1, this embodiment of the present invention provides a system for detecting the location and extent of damage to a buckling restrained brace, which is used to implement the method for detecting the location and extent of damage to a buckling restrained brace described in Example 1. The system includes a sensor and its corresponding magnetic base, a data acquisition system, and an excitation device. The sensor is mounted on the magnetic base, and the data acquisition system is electrically connected to each sensor. A schematic diagram of the detection device is shown in FIG. Figure 6 shown.

[0088] The working principle and process of the buckling restrained brace damage location and degree detection system are as follows: Divide the core component into units every 100 mm, but the total number of units should not be less than 20. Place magnetic bases between the units and bond them to the surface of the core component with adhesive. Install sensors on the magnetic bases and connect the sensors to the data acquisition system via cables. Adjust the data acquisition system parameters: sampling frequency is 5000 Hz; duration is 1 s; the sampling amplitude is determined by the magnitude of the excitation and the distance of the sensor; Three excitations were applied at the middle unit position, and the response signals collected by all sensors were recorded.

[0089] Example 3: Based on Example 1, this embodiment of the present invention details the process for establishing a mathematical function of curvature modal differences, wavelet coefficient differences, and damage values. A fatigue test was performed on a newly manufactured buckling restraint brace. The brace has a total length of 1910 mm, a core section of 1250 mm, a transition section of 45.75 mm, and an elastic section of 230 mm. The brace is made of Q235 steel. Each unit cell of the brace is equipped with strain gauges, and displacement and force sensors are installed around the connecting plate for data acquisition.

[0090] (1) Sensor setting: Each unit cell of the buckling restraint support is equipped with a strain gauge, and displacement and force sensors are installed around the connecting plate for data acquisition.

[0091] (2) Fatigue test: After 30 cycles of loading, the corresponding damage value and the number of loading cycles are shown in Table 1. Three excitations are applied at the middle unit position, and the response signals of all sensors are recorded.

[0092] Table 1 Loading condition record table

[0093] (3) Data acquisition: Apply three excitations at the middle unit position and record the response signals of all sensors.

[0094] (4) Modal analysis: The first-order frequency of the core component is extracted as 434.7 Hz and its modal vibration shape, as shown in the figure.

[0095] (5) Damage identification: At the damage location, the modal curvature difference and wavelet coefficient difference of different working conditions are obtained respectively.

[0096] (6) Establish mathematical model: Establish the mathematical function relationship between curvature modal difference, wavelet coefficient difference and damage value, such as Figure 7 and Figure 8 shown.

[0097] Example 4: Based on Example 1, this embodiment of the present invention provides a detailed description of the process for detecting the location and extent of damage to a buckling restrained brace.

[0098] A nondestructive testing experiment was conducted on a buckling-restrained brace that had been subjected to an earthquake. The brace is 1910 mm long, with a 1250 mm core section, a 45.75 mm transition section, and a 230 mm elastic section. Made of Q235 steel, each unit cell of the buckling-restrained brace was equipped with strain gauges, and displacement and force sensors were installed around the connecting plate for data acquisition.

[0099] (1) Sensor arrangement: The core component is evenly divided into 26 units (one every 50 mm), and the sensors are installed at the unit intervals using magnetic bases and connected to the data acquisition system.

[0100] (2) Parameter setting: sampling frequency 5000 Hz, duration 1 s, sampling amplitude determined by the excitation size and sensor distance.

[0101] (3) Data acquisition: Apply three excitations at the middle unit position and record the response signals of all sensors.

[0102] (4) Modal analysis: The first-order frequency of the core component is extracted as 434.7 Hz and its modal vibration shape, as shown in the figure.

[0103] (5) Damage identification: Calculate the modal curvature difference and wavelet coefficient difference, such as Figure 9 、 Figure 10 and Figure 11 As shown; It is found that there is an obvious mutation at the position of 562mm, and the modal curvature difference is -9.4×10 -5 , the wavelet coefficient difference is -7.05×10 -5 ; According to the mathematical function relationship between the damage value and the curvature mode difference and the damage value and the wavelet coefficient difference, the damage value at this location is calculated to be 0.326 and 0.290.

[0104] (6) Verification results: The data from the strain gauge and displacement force sensor show that the damage location is at 550 mm and the damage value is 0.298, which is highly consistent with the test results and meets the engineering accuracy requirements.

[0105] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for detecting the damage location and extent of a buckling restrained brace, characterized in that: The following steps are involved: The baseline signal of the buckling restrained support under undamaged working conditions is collected, and the signals under various damaged working conditions are obtained through fatigue testing. The baseline signal and the signals under various damaged conditions are subjected to Fourier transform to extract modal features. Based on the modal characteristics, a mathematical relationship model between the modal curvature difference and wavelet coefficient difference and the damage degree is established, where the modal curvature difference and wavelet coefficient difference are the parameter differences between the current working condition and the intact working condition; Collect the actual damaged buckling restraint support signal and extract the modal information of the actual damaged buckling restraint support; Based on the modal information of the actual damaged buckling restrained support, the normal distribution of the modal information is constructed and combined with the curve mutation analysis to determine the damage location, and the modal curvature difference and wavelet coefficient difference corresponding to the damage location are extracted; The damage degree is determined based on the mathematical relationship model between the modal curvature difference, wavelet coefficient difference and damage degree, as well as the modal curvature difference and wavelet coefficient difference corresponding to the damage location; The normal distribution of the modal information is constructed and combined with the curve mutation analysis to determine the damage location, specifically: Obtain the modal characteristics of the intact component and the component to be tested, calculate the modal curvature of the intact component and the component to be tested respectively, and then perform wavelet transform on the modal curvature to enhance the local feature extraction of the modal curvature to obtain the wavelet coefficients of the intact component and the component to be tested; Calculating the modal curvature difference based on the modal curvatures of the undamaged component and the component to be measured, and calculating the wavelet coefficient difference based on the wavelet coefficients of the undamaged component and the component to be measured; Construct the normal distribution of the modal curvature and wavelet coefficients of the intact component and the component to be tested, and then construct the normal distribution of the modal curvature difference and wavelet coefficient difference; Normalizing each parameter in the normal distribution of the modal curvature difference and the wavelet coefficient difference to obtain the standard quantile of the modal curvature difference and the standard quantile of the wavelet coefficient difference; If the standard quantile of the modal curvature difference and the standard quantile of the difference between the wavelet coefficients Stay within the confidence interval, that is, satisfy and When , it is determined that no damage occurs; otherwise, it is determined that damage occurs; The confidence level is The upper quantile of the modal curvature difference, The confidence level is The upper quantile of the wavelet coefficient difference, represents the significance level; The modal curvature difference and wavelet coefficient difference curves are plotted to detect the mutation points in the curves. The mutation points are the damage locations of the buckling restraint support components.

2. The method for detecting the damage location and extent of a buckling restrained brace according to claim 1, characterized in that: The method collects the reference signal of the buckling restrained support under the intact working condition, obtains the signal under each damaged working condition through fatigue testing, and performs Fourier transform on the reference signal and the signal under each damaged state to extract the modal characteristics, specifically: The components of the buckling restraint support are divided into multiple units, magnetic bases are set at the intervals between the units, and sensors are installed on the magnetic bases. The sensors are connected to the data acquisition system through cables. Based on the sampling frequency, duration, and amplitude set by the data acquisition system, sensors are used to collect the baseline signal of the buckling restrained brace under intact working conditions, as well as the signals under various damaged working conditions during the fatigue test. The reference signal and the signals in each damage state are converted into frequency domain signals through fast Fourier transform; Calculate the average spectrum of each frequency domain signal and identify the natural frequency from the average spectrum; Extract the complex response of each measurement point at the identified natural frequency and calculate the amplitude and phase; The point with the maximum amplitude in the average spectrum is selected as the reference point, and the vibration mode value of the reference point is set to 1. The vibration mode values ​​of other positions are the ratios of the amplitudes of other positions to the amplitude of the reference point. The vibration mode direction is determined based on the phase difference between other positions and the reference point. Finally, the complete vibration mode is obtained to complete the modal feature extraction.

3. The method for detecting the damage location and extent of a buckling restrained brace according to claim 2, wherein: The specific calculation formula for converting the signal into the frequency domain by fast Fourier transform is: in, Indicates the first outputs, Indicates the first input samples, represents the number of sample points, Represents an imaginary unit , represents the natural base, Represents pi.

4. The method for detecting the damage location and extent of a buckling restrained brace according to claim 3, wherein: The calculation formula of the amplitude is: in, Indicates the first The amplitude of the output, Indicates the first The real part of the output, Indicates the first The imaginary part of the output; The calculation formula of the phase is: in, Indicates the first The phase angle of the output, Represents the inverse tangent function.

5. The method for detecting the damage location and extent of a buckling restrained brace according to claim 1, wherein: The method for establishing the mathematical relationship model between the modal curvature difference, the wavelet coefficient difference and the damage degree is: The Miner linear damage theory criterion is used to calculate the damage value of each part of the buckling restrained brace; Through fatigue tests, acceleration signals under different fatigue states are obtained. Specifically, the damage value of the buckling restraint support core component in the corresponding state is calculated, and then the modal curvature difference and wavelet coefficient difference under the corresponding damage state are calculated; there is a quadratic function relationship between the damage value and the modal curvature difference and wavelet coefficient difference. The modal curvature difference and wavelet coefficient difference are exponentially fitted, and a fitting equation is established to obtain a mathematical relationship model between the modal curvature difference, wavelet coefficient difference and the damage degree.

6. The method for detecting the damage location and extent of a buckling restrained brace according to claim 5, characterized in that: The damage value of each part of the buckling restrained brace is: in, Indicates the damage value, that is, the degree of damage, To maintain the The number of loading cycles when the component fails at the first stress level, For the The number of loading cycles of the component under the stress level is Indicates the Level stress condition.

7. The method for detecting the damage location and extent of a buckling restrained brace according to claim 1, wherein: The calculation formula of the modal curvature difference is: in, Buckling restrained brace members Level The modal curvature of the element, Buckling restrained brace members Level -1 element modal displacement, Buckling restrained brace members Level The modal displacement of each element, Buckling restrained brace members Level +1 element modal displacement, is the cell length, for Level The modal curvature difference of each element is For the component under test Level The modal curvature of the element, Undamaged components Level The modal curvature of each element; The calculation formula of the wavelet coefficient difference is: in, is the wavelet coefficient, is the complex conjugate of the wavelet function, Indicates the modal curvature with the measuring point position The function of change, is the translation factor, is the change of the measuring point, is the wavelet coefficient difference, is the wavelet coefficient of the component to be tested, is the wavelet coefficient of the undamaged component, Represents the scale index, which is used to control the scaling degree of the wavelet.

8. The method for detecting the damage location and extent of a buckling restrained brace according to claim 7, wherein: The normal distribution of the modal curvature and wavelet coefficients of the intact component and the component to be tested is constructed as follows: in, Buckling restrained brace members Level The mean of the modal curvatures of the elements, Buckling restrained brace members Level The variance of the modal curvature of each element, is the wavelet coefficient The mean of is the wavelet coefficient The variance of Indicates the number of sample points; The normal distribution of the constructed modal curvature difference and wavelet coefficient difference is specifically: in, for Level The mean of the modal curvature differences of the elements, for Level The variance of the modal curvature difference of each element, is the mean of the wavelet coefficient differences, is the variance of the wavelet coefficient difference, For the component under test Level The mean of the modal curvatures of the elements, For the component under test Level The mean of the modal curvatures of the elements, For the component under test Level The variance of the modal curvature of each element, For the component under test Level The variance of the modal curvature of each element, is the mean value of the wavelet coefficients of the component to be tested, is the mean of the wavelet coefficients of the undamaged component, is the variance of the wavelet coefficients of the component to be tested, is the variance of the wavelet coefficients of the undamaged component.

9. The method for detecting the damage location and extent of a buckling restrained brace according to claim 8, wherein: The specific calculation formula for the standard quantile of the modal curvature difference is: in, is the standard quantile of the modal curvature difference; The specific calculation formula for the standard quantile of the wavelet coefficient difference is: in, is the standard quantile of the wavelet coefficient difference, which is used to evaluate the distance between the sample point and the overall mean.

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